Answer:
-5 + 12 i
Step-by-step explanation:
(2 + 3i)^2 = 4 + 6i + 6i + 9i^2
= 4 + 12 i + 9(-1)
= - 5 + 12 i
Find the value of z
[tex]\textsf {Finding y :}[/tex]
[tex]\implies \mathsf {1^{2} + y^{2} = 3^{2}}[/tex]
[tex]\implies \mathsf {y^{2} = 8}[/tex]
[tex]\implies \mathsf {y = 2\sqrt{2}}[/tex]
[tex]\textsf {Finding z :}[/tex]
[tex]\implies \mathsf {(2\sqrt{2})^{2}+8^{2}=z^{2}}[/tex]
[tex]\implies \mathsf {z^{2} = 72}[/tex]
[tex]\implies \mathsf {z = 6\sqrt{2}}[/tex]
Answer:
z =8.49 or 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Do the Pythagorean theorem = [tex]a^{2} +b^{2} =c^{2}[/tex]
Length of hypotenuse = 8+1=9
length of one side = 3
so, a²+3²=9²
a²+3²=9²
a²=81-9
a²=72
a=√72=8.49 or 6[tex]\sqrt{2}[/tex]
The table lists the average monthly cost to workers for family health insurance for various years.
a) Use a graphing calculator to fit a regression line to the data.
b) Predict the average monthly cost to workers for family health insurance in 2021, and compare the value with $510.37, which
is obtained using the points (1,338) and (4,385).
c) Find the correlation coefficient for the regression line, and determine whether the line fits the data closely.
Answer:
5 dollars :)
Step-by-step explanation:
ig
What should be added to (-10) to get (+10)
Answer:
20
Step-by-step explanation:
-10 + 20 = +10
Answer:
[tex]\fbox {20}[/tex]
Step-by-step explanation:
Let the required term be x
Then :
x + (-10) = 10x - 10 = 10x = 10 + 10x = 20Consider the equation. Which graph shows a line that is perpendicular to the line defined by the given equation? A. In a linear graph line diagram, A line passes through (minus 4, minus 2) and (2, minus 0.5) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. B. In a linear graph line diagram, A line passes through (2, 0.5) and (minus 4, 2) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. C. In a linear graph line diagram, A line passes through (2, 4) and (0.5, minus 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units. D. In a linear graph line diagram, A line passes through (2, minus 4) and (0.5, 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units.
The graph second represents the line that is perpendicular to the line y = 4x - 2 option (B) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The question is incomplete:
The complete question is:
Consider the equation y = 4x - 2 Which graph shows a line that is perpendicular to the line defined by the given equation?
Please refer to the attached picture.
The given line:
y = 4x - 2
The slope of the line m = 4
The slope of the line which is perpendicular to the above line:
M = -1/4 = -0.25
The graph second has a slope of -0.25
[tex]\rm y\ -2\ =\ \dfrac{\left(2-0.5\right)}{-4-2}\left(x+4\right)[/tex]
y - 2 = -0.25x - 1
y = -0.25x + 1
Thus, the graph second represents the line that is perpendicular to the line y = 4x - 2 option (B) is correct.
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Help!! Please and thank you!
It is clear that T lies on the perpendicular bisector of NP. See the explanation below.
Given that M (X,Y) is the midpoint of NP
X thus = (5+1)/2
= 3
Y = (7+1)/2
= 4
Hence, we have M (3,4)
Consequent on the above:
Slope TM (m') = (4-2) / (3-6) = - 2/3
Slope of NP (m) = (7-1) / (5-1) = 6/4 = 3/2
M' = -1/m
Hence
TM ⊥ NP; and NP ⊥ TM
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This probability distribution shows
the
typical grade distribution for a Geometry
course with 35 students.
Grade
B
F
Frequency
5
10
15
3
2
Find the probability that a student earns
a
grade of B or C.
p=[?]
Answer:
The probability that a student earns a grade of A is 1/7.
Let E be an event and S be the sample space. The probability of E, denoted by P(E) could be computed as:
P(E) = n(E) / n(S)
As the total number of students = n(S) = 35
Students getting the grade A = n(E) = 5
So, the probability that a student earns a grade of A:
P(E) = n(E) / n(S)
= 5/35
= 1/7
Hence, the probability that a student earns a grade of A is 1/7.
Keywords: probability, sample space, event
Which of the following best describes how the y values are changing over each interval?
X
1
23
3
4
5
y
2
4
8
16
32
O They are increasing by 2 each time.
O They are increasing by 4 each time.
They are being multiplied by 2 each time.
O They are being multiplied by 4 each time.
Answer:
They are being multiplied by 2 each time.
Step-by-step explanation:
The X values are going up by 1 and every time X goes up by 1, Y doubles. So (1,2) goes to (2,4) and then (3,8) etc.
Alec paid the bill for dinner with his clients which totaled $140 before tax and tip. If an 8 percent sales tax was added to the cost of the meal, and an automatic tip was added in the amount of $25.00, what was the total cost of the dinner?
The total cost of the dinner is $176.20.
What is the total cost of the dinner?The total cost of the dinner is the sum of the bill for the dinner, the tax and the tip.
Total cost = tip + bill of the dinner + tip
Tax = 0.08 x 140 = $11.20
Total cost = $140 + $25 + $11.20 = $176.20
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A group of people were given a personality test to determine if they were Type A or Type B. The results are shown in the table below:
Answer choices:
Compare P(Male or Type B) with P(Male | Type B). (5 points)
P(Male or Type B) > P(Male | Type B)
P(Male or Type B) = P(Male | Type B)
P(Male or Type B) < P(Male | Type B)
There is not enough information.
The option third "P(Male or Type B) < P(Male | Type B)" is correct because 0.575 < 0.76
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
P(Male or Type B) = (number of male + number of type B - number that are both)/total population
[tex]\rm = \dfrac{103 + 50- 38}{200 }[/tex]
= 0.575
P(Male | Type B) = (number of male people inside the type B)/(number of Type B people)
= 38/(38 + 12)
= 0.76
0.575 < 0.76
P(Male or Type B) < P(Male | Type B)
Thus, the option third "P(Male or Type B) < P(Male | Type B)" is correct because 0.575 < 0.76
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its math help me out
Answer:
60 minutes
Step-by-step explanation:
we can see that the number of minutes increases by 8 each day
(12 + 8 = 20, 20 + 8 = 28, 28 + 8 = 36...)
So, because we have the value for the previous day (day 6) we know that we can simply add 8
52 + 8 = 60
So, the predicted number of minutes for day 7 is 60
hope this helps!!
Millie needs a total of 7.8 feet of ribbon for a school project. She needs 0.7 more feet of ribbon. How much ribbon, in feet, did Millie already have? Write and solve an equation to find the answer.
6.9
7.1
7.5
8.5
Subtraction is a mathematical operation that reflects the removal of things from a collection. The ribbon that Millie already had is 7.1 feet.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given Millie needs a total of 7.8 feet of ribbon for a school project. Also, She needs 0.7 more feet of ribbon. Therefore, the ribbon that Millie needs is,
Ribbon Millie had = Total Ribbon - ribbon that is needed
= 7.8 feet - 0.7feet
= 7.1 feet
Hence, the ribbon that Millie already had is 7.1 feet.
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Which of the following are solutions to the equation below?
4x^2 + 4x + 1 = 9
Check all that apply
Answer:
Option B and D
Step-by-step explanation:
Subtract 9 from both sides :
4x² + 4x - 8 = 0
Divide both sides by 4 :
x² + x - 2 = 0
Factorise using factorisation method :
x² - x + 2x -2 = 0
x(x - 1) +2(x-1) = 0
(x+2)(x-1) = 0
Solve for x
x +2 = 0 OR x - 1 = 0
x = -2 OR x = 1
Answer will be Option B and D
Hope this helped and have a good day
Answer:
option b. –2 and d. 1 are correct.
*For detailed explanation refer to the attachment
Please help!!!!! ASAP, If you can, i would love the steps on how to do it!! Thanks
Answer:
(5,18) & (-5 , 38)
Step-by-step explanation:
Solutions of linear and quadratic system of equations:A linear equation represented by a line in a graph intersect the quadratic equation represented by a parabola zero, one or two times.
f(x) = x² - 2x + 3 -------------------(I)
f(x) = -2x + 28 ---------------------(II)
x² - 2x + 3 = -2x + 28
x² - 2x + 2x + 3 - 28 = 0
x² - 25 = 0
x² = 25
x = √25 = √5*5
x = ± 5
Plugin x = 5 in equation (II),
f(5) = -2*5 + 28
= -10 + 28
= 18
(5 , 18)
Plugin x = -5 in equation (II),
f(-5) = -2*(-5) + 28
= 10 + 28
= 38
(-5, 38)
Answer:
(5, 18) and (-5, 38)
Step-by-step explanation:
Given system of equations:
1) f(x) = x² - 2x + 3 ⇒ y = x² - 2x + 3
2) f(x) = -2x + 28 ⇒ y = -2x + 28
Solve using the Substitution Method:
Step 1: Substitute the the first equation into the second equation.
⇒ x² - 2x + 3 = -2x + 28
Step 2: Solve for x.
x² - 2x + 3 = -2x + 28 [ Add 2x to both sides. ]
x² - 2x + 2x + 3 = -2x + 2x + 28
⇒ x² + 3 = 28 [ Subtract 28 from both sides. ]
x² + 3 - 28 = 28 - 28
⇒ x² - 25 = 0 [ Factor using the following rule: a² - b² = (a - b)(a + b). ]
(x - 5)(x + 5) = 0
⇒ x - 5 = 0, x + 5 = 0 [ Solve for the values of x. ]
x - 5 + 5 = 0 + 5, x + 5 - 5 = 0 - 5
⇒ x = 5, x = -5
Step 3: Solve for y.
Substitute the found x-values into one of the given equations.
y = x² - 2x + 3 ⇒ y = (5)² - 2(5) + 3 ⇒ y = 25 - 10 + 3 ⇒ y = 18
y = x² - 2x + 3 ⇒ y = (-5)² - 2(-5) + 3 ⇒ y = 25 + 10 + 3 ⇒ y = 38
The solutions to the system of equations are:
⟹ x₁ = 5, y₁ = 18 ⇒ (5, 18)
⟹ x₂ = -5, y₂ = 38 ⇒ (-5, 38)
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For function f(x), which pair of limits would verify the existence of a vertical asymptote at x = –1?
The pair of limits that would verify the existence of a vertical asymptote at x = –1 is:
[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
For a vertical asymptote at x = -1, the denominator is zero at -1, hence both lateral limits at x = -1 go to infinity, that is:
[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]
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slope of (0,1) and (4,3)
Answer:
1/2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-1)/(4-0)
m=2/4
m=1/2
The slope of the given points (0,1) and (4,3) will be ( 1 / 2 ).
What is the slope of the line?
The increase divided by the run, or the ratio of the rise to the run is known as the line's slope. In the coordinate plane, it describes how steep a line is.
The slope of the line is calculated by the formula given below:-
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{3-1}{4-0}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Therefore the slope of the given points (0,1) and (4,3) will be ( 1 / 2 ).
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The table gives the average monthly precipitation, in inches, in Seattle, Washington, from January through July, where January is month 1 and July is month 7. How would you describe the relationship between the variables in the data? Select all that apply.
There is a linear association between the month and average monthly precipitation.
There is a nonlinear association between the month and average monthly precipitation.
As the number of months increases, the average monthly precipitation, in inches, increases.
As the number of months increases, the average monthly precipitation, in inches, decreases.
The relationship between the variables in the data will be as the number of months increases, the average monthly precipitation, in inches, decreases. Then the correct option is D.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The table gives the average monthly precipitation, in inches, in Seattle, Washington, from January through July, where January is month 1 and July is month 7.
Month 1 2 3 4 5 6 7
Average monthly precipitation 5.2 3.9 3.3 2.0 1.6 1.4 0.6
Then the relationship between the variables in the data will be as the number of months increases, the average monthly precipitation, in inches, decreases.
Then the correct option is D.
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There is a basketball court. A basketball, who never misses takes a random shot at the basket. What is the probability that the ball will go into the basket
Answer:
100% probability or 1/1
Step-by-step explanation:
This is because since the basketball NEVER misses, there is no chance the the ball will not go inside the basket, leaving room for only the ball to GO inside the basket. Hope this helps!! :D
On a biased dice the probably of getting a 6 is 4/5 the dice is rolled 500 times estimate how many 6s would be riled
Answer:
400
Step-by-step explanation:
4/5×500
=400 6s would be riled
23.
(05.07 MC)
Use the data in the table to determine the correlation coefficient. (1 point)
Overall Student Average Math Class Average
90 80
95 90
80 90
84 95
75 75
80 85
0.65
0.35
0.30
0.03
The correlation coefficient of the data given in the table, using a calculator, is of 0.35
How to find the correlation coefficient of a data-set using a calculator?To find the coefficient, we need to insert the points (x,y) in the calculator.
In this problem, we have that:
The values of x are: 90, 95, 80, 84, 75, 80.The values of y are: 80, 90, 90, 95, 75, 85.Using a calculator, the coefficient is of 0.35.
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A rectangular prism has a square base with a width of 6 and a volume of 360 cm3. If a square pyramid has a base with the same width and height, what is the volume of the pyramid? Round to the nearest tenth.
The volume of the square pyramid is the one-third of the square prism with same height and base area. Then the volume of the pyramid will be 120 cubic cm.
What is the volume of the pyramid?Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.
Then the volume of the pyramid will be
V = (L × B × H) / 3
The volume of the square prism will be
V = (L × B × H)
Then the volume of the square pyramid is the one-third of the square prism with same height and base area.
[tex]\rm V_{pyramid} = \dfrac{V_{prism} }{3}[/tex]
A rectangular prism has a square base with a width of 6 and a volume of 360 cm³.
If a square pyramid has a base with the same width and height.
Then the volume of the pyramid will be
V = 360 / 3
V = 120 cubic cm
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$10,000 is invested at 7% annual interest which is compounded continuously what is the balance after eight years with no deposits or withdrawals are made
Answer:
$17,506.73
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)Given:
P = $10,000r = 7% = 0.07t = 8 yearsSubstitute the given values into the formula and solve for A:
[tex]\sf \implies A=10000e^{(0.07 \times 8)}[/tex]
[tex]\sf \implies A=10000e^{0.56}[/tex]
[tex]\implies \sf A=17506.725...[/tex]
Therefore, the value of the account after 8 years is $17,506.73 to the nearest cent.
Describe the transformations of the graph of y=5 times 2^x-2+3 as compared to the graph of y=2^x
the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.Which transformations are used?
We start with the function:
[tex]f(x) = 2^x[/tex]
And we have the transformed function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Bow, let's start with the original function f(x). If first we apply a vertical dilation of scale factor 5, then we have:
g(x) = 5*f(x).
Then we apply a shift of 2 units to the right, so we have:
g(x) = 5*f(x - 2)
Then we apply a shift of 3 units up, so we have:
g(x) = 5*f(x - 2) + 3
Replacing f(x) by the actual function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Then the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.If you want to learn more about transformations:
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Solve the compound inequality for x and identify the graph of its solution.
x+7>3 and x-5≤-1
O A. Solution: x<-4 or x ≥ 4
-5-4-3 -2 -1 0 1 2 3 4 5
OB. Solution: x>-4 and x≤ 4
-5-4-3 -2 -1 0 1 2 3 4 5
O C. Solution: x>-4 and x≤ 4
-5 -4 -3 -2 -1 0 1 2 3 4 5
OD. Solution: x²-4 and x < 4
Answer:
C is the answers for the question
Step-by-step explanation:
please mark me as brainlest
A group of 328 people consists of men ,women, and children. There are five times as many men than children and twice as many women then children. How many women are there
Step-by-step explanation:
Ultimately we know:
Men = * 5
Women = * 2
Children =
We can already make the estimation that the amount of children will be below 50. So by trial and error you will get to your answer by substituting with 41.
Children - 41
Women - 41 x 2 = 82
Men - 41 x 5 = 205
205 + 41 + 82 = 328
So your answer is 41
Need help and a better understanding
79=11x+13
Solve each equation by using the properties of equality and justify each step
Solution: X=6
Detailed explanation:
In this problem we're asked to find "x" or the unknown.
The first step is to subtract 11x from both sides.
[tex]---\mapsto\boldsymbol{-11x+79=13}[/tex]
Next, subtract 79 from both sides.
[tex]---\mapsto\boldsymbol{-11x=-66}[/tex]
To finish this off, divide both sides by -11.
[tex]---\mapsto\boldsymbol{x=6}[/tex]
Voila! There's our answer!
Cheers!! ^-^___________________
Hope I helped. Best wishes.
Reach far. Aim high. Dream big.
___________________
[tex]\large\green\longrightarrow \tt \large \:79 \: = \: 11x \: + \: 13[/tex]
[tex]\large\green\longrightarrow \tt \large \:79 \: - \: 13 \: = \: 11x[/tex]
[tex]\large\green\longrightarrow \tt \large \:66 \: = \: 11x[/tex]
[tex]\large\green\longrightarrow \tt \large \: \frac{ \cancel{66} \: \: ^{ \pink6} }{ \cancel{11}} \: = \: x \\ [/tex]
[tex]\large\green\longrightarrow \tt \large \:6 \: = \: x[/tex]
Hence , the value of x is 6
Venn diagram in maths ! !
Answer:
People surveyed: 79
a) p(s) = 46/79
b) p(snv) = 13/79
c) p(suv) = 96/79
hope this helps, and tell me if you get it right! It's prob wrong though, im bad at venn diagrams (×_×)⌒☆
The equation y = 180 + 5x represents the amount a school club will pay a T-shirt company for custom T-shirts, where x represents the number of T-shirts purchased and y represents the total cost in dollars. The equation y = 10x represents the club’s income from selling the T-shirts, where y represents the money earned in dollars and x represents the number of T-shirts sold. Assuming that the club members sell all the T-shirts they purchase, when will the club make a profit? The following graph represents this situation:
Answer:
36 TSHIRTS is the number for minimum profit
Step-by-step explanation:
Y = Y
180 + 5X = 10X
180 = 10X - 5X
180 = 5X
X = 180/5
X = 36
Help me pls. I need the answer so i can get a good grade and get my math credit
Answer:
D
Step-by-step explanation:
the zero is the value of x where the line crosses the x- axis, that is
zero is x = - 2
Function h is a transformation of the parent exponential function. Which statement is true about this function?
As x approaches positive infinity, approaches 0.
As x approaches negative infinity, approaches positive infinity.
As x approaches positive infinity, approaches positive infinity.
As x approaches negative infinity, approaches negative infinity.
The statement that is true about this function is C. As x approaches positive infinity, h(t) approaches positive infinity
Calculations and Parameters
Given that we have:
The domainThe rangeThe functionTherefore, when x approaches to negative infinity,
[tex]\lim_{x \to \infty} h(x)[/tex]
= 2^(-∞-5)
= 2^(-∞)
= 1/2^∞
=0
Also, as x approaches negative infinity, function h(x) approaches 0.
Then when x approaches to positive infinity,
[tex]\lim_{x \to \infty} h(x)[/tex]
2^(∞-5)
= 2^(∞)
= ∞
Therefore, As x approaches positive Infinity, h(x) approaches positive infinity.
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